We revisit guided-filter-based joint upsampling (GIJU) from both empirical and theoretical perspectives. First, we present a systematic empirical finding that GIJU consistently achieves its highest accuracy with the smallest tested filter radius across the evaluated tasks and scales. To explain this, we provide a theoretical analysis that exposes a previously implicit approximation error in the GIJU pipeline. We formalize this error as a local covariance term between the guide image and the coefficient field, whose magnitude is bounded by local variances, thus clarifying why reducing the effective support improves accuracy. Third, motivated by this insight, we introduce Gaussian-weighted GIJU. By replacing the standard box filter with Gaussian weights, our method further reduces the effective filter support, directly mitigating the identified covariance error. Extensive experiments on 100 images for colorization and L0 smoothing, as well as on 100 image pairs for depth upsampling, demonstrate that our method consistently outperforms conventional GIJU and a recent filter-based baseline, Detail-preserving Joint Image Upsampling (DPJIU), particularly around edges. Diagnostic analyses, including sensitivity maps and synthetic stepedge experiments, validate the connection between our theory and its practical benefits. Our work provides both a deeper understanding of GIJU and a practical, high-performance, training-free joint upsampler.
SHIMIZU et al. (Thu,) studied this question.